This may come as a surprise to some who are used to hearing ACT for Depression, ACT for Anxiety, etc. The actual wording, from a functional contextual point of view, is Psychological Flexibility with Depression, Psychological Flexibility with Anxiety, etc.
What is psychological flexibility?
ACT is based on Relational Frame Theory (RFT), a theory of human language and cognition, and 'cognition' is essentially language turned inward. Language probably evolved for social reasons: me talking to you. However, language has obviously gone inward and humans now have a 'me to me' language called cognition. We think of the past, the future and the present and have feelings that are related to all of those thoughts. We also do lots of problem solving "in our heads," from simple arithmetic to inventing spaceships. It's easy for all of us to get stuck in our heads and not paying attention to the physical world in the present moment. Some folks are more stuck "in their mind" than others, but the basic process of influencing others toward psychological flexibility is the same for all.
The trick is to be in our heads when needed AND paying attention to the physical world when needed, and the ability to effectively shift from one to the other (or do both at once) is called Psychological Flexibility. Steve Haye's popular book is called Get Out of Your Mind and into Your Life.
Both the Matrix and Hexaflex diagrams give a visual representation of this "get out of your mind" process. The lower parts are 'mindy' stuff and the upper are sensory stuff. If you stare at the lower part of the diagram you miss the upper part. The opposite is also true, but there are not many people who report having a problem with too much contact with the physical present moment.
Kevin L. Polk, Ph.D.
Training individuals and groups
Psychological Flexibility Book: http://www.amazon.com/dp/B004M8S4Z4